Now, the drop shadow offset moves along with the rotation such that the shadow always appears in the right place.
It worked, and we moved on.

Now that I understand JavaFX and the scenegraph a bit better I realize that this approach is wrong - there's a much simpler solution!
We don't want to apply the drop shadow to the Path object directly, since the path is what we are rotating with our minute angle.
Instead, we should simply move the effect out to the surrounding parent. That will apply the drop shadow after the shape
has been rotated.
Doing that, we can set our drop shadow initialization back to the original simple 5,5 delta, and we get exactly the result we want:

So, think about which node you apply effects to! And by the way, the effects framework is really fun to play with - you should definitely
explore javafx.scene.effect.\* !